1) I work in IT in the motortrade and know just how easily it is to get key and alarm codes plus owners home address from the myriad of systems that hold that information. Some of which is not very secure at all. There are about 100K people in the UK with access to this data and odds are that at least some are corrupt and willing to sell the data to car thieves. Especially important with classic cars such as my Land Rovers that are amongst the most stolen vehicles in UK.
2) If a criminal steals a car and wants to put fake plates on it they can quickly browse an owners forum like this and find a matching vehicle and simply use that plate. Sure they could see the plate while driving around but it is far quicker and cheaper for them to find one online. Especially true when they want to clone a plate for use in drive off refuelling/petrol theft.
Better safe than sorry, always safer to hide regno. Don't make the criminals life easy!